Resonant multiple wave, multi-lump wave and complex <i>N</i> -soliton solutions to the (3+1)-dimensional Jimbo–Miwa equation

The main idea of this paper is to look into some novel exact wave solutions of the [Formula: see text]-dimensional Jimbo–Miwa equation (JME) that has a major role in the fields of fluid mechanics and physics. Based on the Hirota bilinear form (HBF) obtained by the Cole–Hopf transformation, the weight algorithm (WA) combined with the linear superposition theory (LST) is employed to develop the resonant multiple wave solutions (RMWSs). In addition, the multi-lump wave solutions are derived via adopting the homoclinic test approach. Finally, the complex N-soliton solutions (CNSSs) are also probed through the HBF. The graphical descriptions of the corresponding exact solutions are displayed to present the physical attributes by choosing the reasonable parameters. The findings in this paper are all new, which can help us make sense of the nonlinear dynamic behaviors of the considered equation better.